Parameter Estimation Research Articles

Estimation of the constant-stress model with bathtub-shaped failure rates under progressive type-I interval censoring scheme

This paper investigates constant-stress accelerated life tests interrupted by a progressive type-I interval censoring regime. We provide a model based on the Chen distribution with a constant shape parameter and a log-linear connection between the scale parameter and stress loading. Inferential methods, whether classical or Bayesian, are employed to address model parameters and reliability attributes. Classical methods involve the estimation of model parameters through maximum likelihood and midpoint techniques. Bayesian approximations are achieved via the utilization of the Metropolis–Hastings algorithm, Tierney-Kadane procedure, and importance sampling methods. Furthermore, we engage in a discourse on the estimation of confidence intervals, making references to both asymptotic confidence intervals and credible intervals. To conclude, we furnish a simulation study, a corresponding discussion, and supplement these with an analysis of real data.

Parameters estimation of complex solar photovoltaic models using bi-parameter coordinated updating L-SHADE with parameter decomposition method

Accurate estimation of unknown parameters of complex photovoltaic models is crucial to whether photovoltaic generators can efficiently convert energy. When a photovoltaic model has multiple diode branches, its complexity increases geometrically. To address the problems of high complexity and difficulty in estimation, this paper proposes an effective improved algorithm based on success-history adaptation differential evolution with linear population size reduction (L-SHADE)—Bi-parameter coordinated updating L-SHADE with parameter decomposition method (CSpL-SHADED). First in CSpL-SHADED, dynamic crossover rate ranking technology is developed to bridge the relationship between individuals and crossover rates, thereby improving effective mutation capabilities. In addition, a dynamic sub-population mechanism is also proposed to divide the entire population into multiple sub-populations so that they are evenly distributed in the search space, so the search ability of individuals in local areas is improved. Secondly, the unknown parameters of solar photovoltaic models of different complexity are effectively decomposed into linear and nonlinear parameters by the decomposition method. The nonlinear parameters are accurately estimated by CSpL-SHADED, and the linear parameters are calculated based on the constructed matrix equation. Through experiments on four solar photovoltaic models of different complexity, CSpL-SHADED showed strong competitiveness to varying degrees compared to the comparative algorithms.

Differential Model-Based Parameter Estimation of IPMSMs From Multi-State Measurements

Differential Model-Based Parameter Estimation of IPMSMs From Multi-State Measurements

An Improved Nutcracker Optimization Algorithm for Discrete and Continuous Optimization Problems: Design, Comprehensive Analysis, and Engineering Applications

This study is presented to examine the performance of a newly proposed metaheuristic algorithm within discrete and continuous search spaces. Therefore, the multithresholding image segmentation problem and parameter estimation problem of both the proton exchange membrane fuel cell (PEMFC) and photovoltaic (PV) models, which have different search spaces, are used to test and verify this algorithm. The traditional techniques could not find approximate solutions for those problems in a reasonable amount of time, so researchers have used metaheuristic algorithms to overcome those shortcomings. However, the majority of metaheuristic algorithms still suffer from slow convergence speed and stagnation into local minima problems, which makes them unsuitable for tackling these optimization problems. Therefore, this study proposes a robust improved nutcracker optimization algorithm (INOA) for better solving those problems in an acceptable amount of time. INOA is based on improving the performance of the standard algorithm using a newly proposed convergence improvement strategy that aims to improve the convergence speed and prevent stagnation in local minima. This algorithm is first applied to estimating the unknown parameters of the single-diode, double-diode, and triple-diode models for a PV module and a solar cell. Second, four PEMFC modules are used to further observe INOA's performance for the continuous optimization challenge. Finally, the performance of INOA is investigated for solving the multi-thresholding image segmentation problem to test its effectiveness in a discrete search space. Several test images with different threshold levels were used to validate its effectiveness, stability, and scalability. Comparison to several rival optimizers using various performance indicators, such as convergence curve, standard deviation, average fitness value, and Wilcoxon rank-sum test, demonstrates that INOA is an effective alternative for solving both discrete and continuous optimization problems. Quantitively, INOA could solve those problems better than the other rival optimizers, with improvement rates for final results ranging between 0.8355% and 3.34% for discrete problems and 4.97% and 99.9% for continuous problems.

Deep estimation of the intensity and timing of natural selection from ancient genomes.

Leveraging past allele frequencies has proven to be key for identifying the impact of natural selection across time. However, this approach suffers from imprecise estimations of the intensity (s) and timing (T) of selection, particularly when ancient samples are scarce in specific epochs. Here, we aimed to bypass the computation of allele frequencies across arbitrarily defined past epochs and refine the estimations of selection parameters by implementing convolutional neural networks (CNNs) algorithms that directly use ancient genotypes sampled across time. Using computer simulations, we first show that genotype-based CNNs consistently outperform an approximate Bayesian computation (ABC) approach based on past allele frequency trajectories, regardless of the selection model assumed and the number of available ancient genotypes. When applying this method to empirical data from modern and ancient Europeans, we replicated the reported increased number of selection events in post-Neolithic Europe, independently of the continental subregion studied. Furthermore, we substantially refined the ABC-based estimations of s and T for a set of positively and negatively selected variants, including iconic cases of positive selection and experimentally validated disease-risk variants. Our CNN predictions support a history of recent positive and negative selection targeting variants associated with host defence against pathogens, aligning with previous work that highlights the significant impact of infectious diseases, such as tuberculosis, in Europe. These findings collectively demonstrate that detecting the footprints of natural selection on ancient genomes is crucial for unravelling the history of severe human diseases.

Power modified XLindley distribution: Statistical properties and applications.

This research introduces a novel two-parameter distribution, the power-modified XLindley distribution, developed through the application of power transformation techniques to the existing modified XLindley distribution. This new distribution enhances flexibility and adaptability in statistical modeling. We conduct a thorough examination of its statistical properties, exploring its potential to improve data fitting and modeling accuracy. To assess the effectiveness of the model, we employ multiple estimation techniques and evaluate their performance through extensive simulation experiments. Our findings indicate that the maximum product of the spacings method is particularly effective for parameter estimation. To demonstrate the practical utility of the proposed model, we apply it to two real-world datasets: one related to flood data and the other to reliability engineering. The results underscore the distribution's superior ability to capture the characteristics of these datasets compared to existing models, highlighting its significance for applications in natural disaster analysis and reliability studies.

The reliability and validity of rapid transcranial magnetic stimulation mapping for muscles under active contraction.

Rapid mapping is a transcranial magnetic stimulation (TMS) mapping method which can significantly reduce data collection time compared to traditional approaches. However, its validity and reliability has only been established for upper-limb muscles during resting-state activity. Here, we determined the validity and reliability of rapid mapping for non-upper limb muscles that require active contraction during TMS: the masseter and quadriceps muscles. Eleven healthy participants attended two sessions, spaced two hours apart, each involving rapid and 'traditional' mapping of the masseter muscle and three quadriceps muscles (rectus femoris, vastus medialis, vastus lateralis). Map parameters included map volume, map area and centre of gravity (CoG) in the medial-lateral and anterior-posterior directions. Low to moderate measurement errors (%SEMeas = 10-32) were observed across muscles. Relative reliability varied from good-to-excellent (ICC = 0.63-0.99) for map volume, poor-to-excellent (ICC = 0.11-0.86) for map area, and fair-to-excellent for CoG (ICC = 0.25-0.8) across muscles. There was Bayesian evidence of equivalence (BF's > 3) in most map outcomes between rapid and traditional maps across all muscles, supporting the validity of the rapid mapping method. Overall, rapid TMS mapping produced similar estimates of map parameters to the traditional method, however the reliability results were mixed. As mapping of non-upper limb muscles is relatively challenging, rapid mapping is a promising substitute for traditional mapping, however further work is required to refine this method.

Lessons learned during a 12-year monitoring project with the endangered Magdalena River turtle (Podocnemis lewyana): hunting pressure, habitat degradation, and methodological considerations.

Turtle species in the Family Podocnemididae, including the Colombian endemic and critically endangered Magdalena River Turtle Podocnemis lewyana, characteristically present low recapture rates that preclude estimation of population parameters using maximum likelihood modeling. In our 12-year monitoring project with this species, we evaluated changes in relative abundances, proportions of sex/size classes, and individual body sizes and body conditions in a population in four channels in the middle Magdalena River drainage. We also inspected for associations between trends in changes in these variables and differences in hunting pressure and habitat degradation. To inspect for temporal and spatial demographic dynamics, we estimated variation in relative abundances using the Catch Per Unit Effort index, the total number of turtles captured over an entire 5-day sampling period using ten baited funnel traps. Relative abundances and the proportions of sex/size classes were different between sites and years. We found a significant decline in the proportion of females and juveniles over time, along with evidence that the females still present were smaller in body size. Our results support the hypothesis that hunting eliminates adult females from these sites, perhaps also translating into a reduction in recruitment. The lack of evidence of generalized declines in body condition of all size classes suggests that habitat degradation might contribute less to the population declines in this region. Our results also illustrate that even when recapture rates are low, monitoring turtles via standardized trapping may yield insights into the population's conservation status that other relative abundance indices cannot.

Using the Nanogonal Membership Function and Fuzzy Parameters for The Exponential-Rayleigh Distribution of Coved-19

In this paper, we discuss estimating the fuzzy parameters of the Exponential-Rayleigh distribution using the Progressive Censored sample for the Rank Set method to become the proposed Rank Set Sampling estimation Method (RSSEM) in Censoring sample using the Newton-Raphson method to determine the parameter estimate values. Then utilizing Al Karkh General Hospital-Ministry of Health and Environment in Iraq for providing information about the actual data for COVID-19. To ascertain the Chi-square test was used. The distribution of the using sample is the Exponential-Rayleigh distribution. (ER). Then, we estimate the probability density function, hazard function, and survival function. To follow the estimation of the parameters and ER distribution's fuzzy parameters, we use the suggested approach. Moreover, to find the efficiency of the estimators, we use the mean square error of the survival function:

Parameters estimation of the Weibull law for reliability modeling of an equipment

Parameters estimation of the Weibull law for reliability modeling of an equipment

Minimizing distance between distribution functions: discrete counterparts to continuous random variables with applications in non-life insurance and stochastic reliability

In this work, we propose a novel family of procedures for deriving a discrete counterpart to a continuous probability distribution. They are based on a class of distances between cumulative distribution functions, including the Cramér, the Cramér-von Mises, and the Anderson-Darling distances as particular cases. The discrete counterpart is defined and derived as the random variable which minimizes its distance to the assigned continuous probability distribution among all the discrete random variables supported on the set of integers (or positive integers). Applications are provided with reference to the exponential and the normal distributions, among others; the discrete counterparts are derived, and their main properties are discussed, also in comparison with the one obtained through an existing discretization technique based on the preservation of the cumulative distribution function at integer values. Parameter estimation for these discrete analogs is discussed, along with an analysis of two real datasets, where they are compared in terms of goodness-of-fit with some popular discrete distributions. Furthermore, in order to highlight the effectiveness and the benefits derived from the proposed discretization procedures, we illustrate two practical applications in actuarial science and in reliability engineering. In the former case, the problem of determining the distribution of the total claims amount for a non-life insurance portfolio is considered, where the claim sizes can be modelled as iid random variables, and the number of claims is random as well. Actuaries use a recursive calculation method based on Panjer's formula, which requires an appropriate discretization of the individual claim distribution, and therefore the proposed procedures can be used. Since we consider two simple cases where the distribution of the total claims amount is analytically acquirable, the efficacy of the discretization procedures in the final approximation can be easily assessed and turns out to be satisfactory, especially when compared to the existing discretization. The latter case considers the determination of the reliability parameter for a complex stress-strength model. Here, the approximation by discretization is compared to Monte Carlo simulation and shown to be relevant: with a comparable if not smaller computational effort, discretization leads to similar results as simulation. Such discretizations can also naturally be applied to more complex problems such as scenario generation in stochastic programming. R code for this article is provided as supplementary material.

Bayesian estimation of some reliability characteristics for Nakagami model using adaptive progressive censoring

The focus of this research is to clarify both conventional and Bayesian parametric estimation methods for the Nakagami distribution making use of adaptive progressive Type II censored data. From a classical estimation perspective, two estimation methods are considered: maximum likelihood and least squares estimations. Along with the model parameters, three reliability metrics are estimated using point and interval estimation. Bayes estimates with gamma and inverse gamma priors are investigated by employing the squared error loss function. The Bayes computations are created using the Markov Chain Monte Carlo technique. Moreover, the classical and Bayesian intervals are also taken into consideration. For evidence of the effectiveness of the given methodologies, a simulation study and three applications from the physics, chemistry, and engineering domains are explored. Lastly three optimality criteria are applied to the stated data sets to pick the best progressive censoring strategy.

Addressing Autocorrelation, Multicollinearity, and Heavy-Tail Errors in the Linear Regression Model

The most popular estimator for estimating parameters of linear regression models is the Ordinary Least Squares (OLS) Estimator. The OLS is considered the best linear unbiased estimator when certain assumptions are not violated. However, when autocorrelation, multicollinearity, and heavy-tail error are jointly present in the dataset, the OLS estimator is inefficient and imprecise. In this paper, we developed an estimator of linear regression model parameters that jointly handle multicollinearity, autocorrelation, and heavy tail errors. The new estimator, LADHLKL, was derived by combining the Hildreth-Lu (HL), the Kibria Lukman (KL), and the Least Absolute Deviation (LAD) estimators. The LADHLKL poses both the characteristics of the LAD, HL, and KL estimators which makes it resistant to both problems. We examined the properties of the proposed estimator and compared its performance with other existing estimators in terms of mean square error. An application to real-life data and simulation study revealed that the proposed estimator dominates other estimators in all the considered conditions in terms of mean square error.

Dry inside: progressive unsaturation within leaves with increasing vapour pressure deficit affects estimation of key leaf gas exchange parameters.

Climate change not only leads to higher air temperatures but also increases the vapour pressure deficit (VPD) of the air. Understanding the direct effect of VPD on leaf gas exchange is crucial for precise modelling of stomatal functioning. We conducted combined leaf gas exchange and online isotope discrimination measurements on four common European tree species across a VPD range of 0.8-3.6 kPa, while maintaining constant temperatures without soil water limitation. In addition to applying the standard assumption of saturated vapour pressure inside leaves (ei), we inferred ei from oxygen isotope discrimination of CO2 and water vapour. ei desaturated progressively with increasing VPD, consistently across species, resulting in an intercellular relative humidity as low as 0.73 ± 0.11 at the highest tested VPD. Assuming saturation of ei overestimated the extent of reductions in stomatal conductance and CO2 mole fraction inside leaves in response to increasing VPD compared with calculations that accounted for unsaturation. In addition, a significant decrease in mesophyll conductance with increasing VPD only occurred when the unsaturation of ei was considered. We suggest that the possibility of unsaturated ei should not be overlooked in measurements related to leaf gas exchange and in stomatal models, especially at high VPD.

Assessing the influence of land use/land cover dynamics and climate change on water resources in Upper Blue Nile, Ethiopia

ABSTRACT This study evaluates the impact of climate and land use changes on the Lake Tana Basin's hydrology, using datasets on land use, weather patterns, topography, soil characteristics, and discharge. Future climate data were obtained from Global Climate Models (GCMs) from the Coupled Model Intercomparison Project Phase Five (CMIP5) and generated using the Weather Generator (LARS-WG) tool from the Long Ashton Research Station with five distinct GCMs. Land use changes were projected using the Markov chain model based on cellular automata (CA). The Soil and Water Assessment Tool (SWAT) model was used to assess changes in hydrological elements between reference and future periods, with calibration and validation ensured by the Integrated Parameter Estimation and Uncertainty Analysis Tool (IPEAT). Projections indicate a 4.9 °C increase in ensemble mean annual temperature and a 16% rise in precipitation by the end of the 21st century under Representative Concentration Pathway (RCP) 8.5. Additionally, average annual hydrological components, including water yield, soil water, percolation, lateral flow, runoff, and actual and potential evapotranspiration, are expected to increase due to combined climate and land use changes. Therefore, it is crucial to fully understand these cumulative impacts before formulating and implementing water resource management strategies in the basin.

External parameter calibration of laser scanner based on the combination of plane-control-based and plane-constraints-based methods

Accurate calibration of the external parameters of a laser scanner is crucial to ensure consistency in data representation from multiple sources. Plane features, known for their simplicity and ease of extraction, are widely used in external parameter calibration. The use of control planes with known plane parameters enables the simultaneous estimation of both translation and rotation parameters, while the use of planes with unknown parameters allows for efficient self-calibration. In this paper, we introduce a novel method that combines the strengths of both types of plane calibration methods to calibrate the external parameters of a laser scanner. The approach, with the help of a Gauss-Helmert adjustment model, integrates control and constraint planes to calibrate the external parameters. The method boasts the ease and accessibility offered by the plane constraint method, utilizing fewer control features while successfully estimating the external parameters of the laser scanner. To evaluate the feasibility of this method, two sets of 12 calibration experiments were conducted on the mobile measurement system platform. Notably, the residual Root Mean Square Errors (RMSE) obtained from these experiments were comparable to those achieved using traditional plane-control-based method. Furthermore, the external parameter correlation aligns with that obtained using the plane-control-based method, while the plane parameter correlation exhibits similarity to that obtained using the plane-constraint-based method. These results confirm that our method effectively minimizes the requirement for control features and enables more convenient calibration of the external parameters of the laser scanner.

Predicting reaction rate constants of organic compounds with oxidants in the atmospheric aqueous-phase through multi-task learning

The atmospheric aqueous-phase chemistry has received increasing attention in the last decades for its non-negligible environmental significance. Yet, the insufficient experimental data on oxidative reaction rate constants (kaq) obstructs the further analysis and modeling of this system. Predictive models based on machine learning (ML) algorithms have shown potential as an effective estimation tool, however, they are restricted to the lack of training data as well. To overcome this data limitation, we developed multi-task (MT) models that could exploit the common knowledge from reactions in gas- and aqueous-phases simultaneously. Toward kaq of organic compounds with hydroxyl radical (OH), nitrate radical (NO3), and ozone (O3), the MT models showed a notably better predictive ability compared to benchmark models, while obtaining wide applicability on compounds from different chemical classes. By interpreting the models using Shapley additive explanations (SHAP), we evidenced that the MT models utilized the common knowledge in both phases and correctly identified the reaction mechanisms. This study aims to provide new insight into the estimation of necessary kinetic parameters in atmospheric aqueous-phase chemistry, as well as a reference to ML research for other predictive tasks of atmospheric interest.

Modeling and analysis of a two-strain immuno-epidemiological model with reinfection

In this paper, we formulate a two-strain model with reinfection that combines immunological and epidemiological dynamics across scales, using the COVID-19 pandemic as a case study. Firstly, we conduct a qualitative analysis of both within-host and between-host models. For the within-host model, we prove the existence and stability of equilibria, and Hopf bifurcation occurs from the infection equilibrium with immune response. This implies that, under specific immune states, the virus within an infected individual may persist, and its concentration may also oscillate periodically. For the between-host model, the disease-free equilibrium always exists and is locally asymptotically stable when the epidemiological basic reproduction number ℜ0<1. In addition, the model can have boundary equilibria of strain 1 or strain 2, which are locally asymptotically stable under specific conditions. However, the co-existence equilibrium does not exist. Secondly, to explore the infection and transmission mechanisms of two strain models and obtain reliable parameter values, we utilize statistical data to fit the immuno-epidemiological model. Simultaneously, we conduct an identifiability analysis of the immuno-epidemiological model to ensure the robustness of the fitted parameters. The results demonstrate the reliable estimation of parameter ranges for structurally unidentifiable parameters with minor measurement errors using the affine invariant ensemble Markov Chain Monte Carlo algorithm (GWMCMC). Moreover, simulations illustrate that enhancing treatment of patients infected with BA.2 strains to inhibit the number of viruses released by infected cells can significantly reduce disease spread.

Exploring shared frailty models for cluster-specific risk estimation: A study on diabetes patients with a history of acute coronary syndrome

This study proposes the use of semiparametric log-normal shared frailty models to analyze time-to-event data for individuals with similar features referred to as clusters. Shared frailty models are useful for modeling and estimating common risk in the lifetimes of individuals in these clusters. While various methods have been proposed for estimating shared frailty models, few studies have explored the use of the pseudo-full-likelihood method. In this study, the pseudo-full-likelihood and hierarchical likelihood approaches were used to construct and estimate parameter estimates and check for asymptotic properties via simulations. Log-normal semiparametric frailty model was used to obtain cluster-specific frailty based on the semiparametric log-normal shared frailty distribution. The results of both methods were compared, and prediction intervals for a random effect were obtained. To further investigate the existence of shared frailty in diabetes patients and a history of acute coronary syndrome (STEMI and NSTEMI), data from UK Biobank was used. The results suggest the presence of frailty within the clusters and indicate cluster time dependence in the study population. Overall, this study highlights the potential benefits of using the pseudo-full-likelihood method in shared frailty modeling and provides insights into the impact of observed variabilities on hazards within clusters.

Modeling insurance loss data using novel approach of moment exponential model: Inference, actuarial measures and application

Asymmetrical probability models are helpful for analyzing skewed data sets since they allow you to describe the form of the distribution and anticipate the chance of extreme events. This article defines a novel approach to continuous moment exponential distribution called the exponentiated generalized moment exponential model. The extension has two additional parameters accounting for the distribution’s shape. We extend this distribution probability density, cumulative distribution, hazard rate, and survival functions and establish different key statistical properties. Parameter estimation is obtained using different procedures, notably maximum likelihood estimation, least square, and Bayesian methods. A Monte Carlo simulation experiment is conducted to assess parameter performance and indicator risk measures. This article examines two distinct actual data sets in order to highlight the significance of the proposed model as well as its application in a variety of settings. The new model is compared to a large number of well-known extensions that were developed by other businesses.